Reflection by Spherical Mirrors and Mirror Formula

Reflection by Spherical Mirrors and Mirror Formula

A glass slab (\( n = 1.5 \)) of thickness \( 15 \, \text{cm} \) is placed over a pin. By how much does the pin appear ra

**Concave mirror image formation** depends on object position: beyond C real inverted diminished between F and C, at C real inverted same size at C, between C and F real inverted magnified beyond C, at F image at infinity, within F virtual erect magnified behind mirror. Shift = t ( 1 - (1/n) ) . t = 15 cm , n = 1.5 . Shift = 15 ( 1 - (1/1.5) ) = 15 ( 1 - (2/3) ) = 15 × (1/3) = 5 cm . Substituting values gives 5 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v

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Reflection by Spherical Mirrors and Mirror Formula

A concave mirror of focal length \( 8 \, \text{cm} \) has an object placed \( 16 \, \text{cm} \) from it. What is the im

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Focal length: f = -8 cm (concave mirror). Object distance: u = -16 cm . Mirror equation: (1/v) + (1/u) = (1/f) . (1/v) + (1/-16) = (1/-8) ⇒ (1/v) = (1/-8) + (1/16) = (-2 + 1/16) = (-1/16) . v = -16 cm (real image). Substituting values gives 16 cm, which matches expected image

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Reflection by Spherical Mirrors and Mirror Formula

An object is placed \( 24 \, \text{cm} \) from a concave mirror of focal length \( 12 \, \text{cm} \). What is the image

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. Focal length: f = -12 cm , u = -24 cm . Mirror equation: (1/v) + (1/-24) = (1/-12) ⇒ (1/v) = (1/-12) + (1/24) = (-2 + 1/24) = (-1/24) . v = -24 cm (real image). Substituting values gives 24 cm, which matches expected image position

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Reflection by Spherical Mirrors and Mirror Formula

A glass slab (\( n = 1.5 \)) of thickness \( 7.5 \, \text{cm} \) is placed over a point. What is the apparent shift?

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Shift = t ( 1 - (1/n) ) . t = 7.5 cm , n = 1.5 . Shift = 7.5 ( 1 - (1/1.5) ) = 7.5 ( 1 - (2/3) ) = 7.5 × (1/3) = 2.5 cm . Substituting values gives 2.5 cm, which matches expected image position and magnification from mirror/lens formula

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Reflection by Spherical Mirrors and Mirror Formula

An object is placed \( 10 \, \text{cm} \) from a convex mirror of focal length \( 15 \, \text{cm} \). What is the image

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Focal length: f = 15 cm , u = -10 cm . Mirror equation: (1/v) + (1/-10) = (1/15) ⇒ (1/v) = (1/15) + (1/10) = (2 + 3/30) = (5/30) = (1/6) . v = 6 cm (virtual image). Substituting values gives 6 cm, which matches expected image position and magnification from mirror/lens formula 1/f

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Reflection by Spherical Mirrors and Mirror Formula

A concave mirror of focal length \( 10 \, \text{cm} \) forms an image \( 20 \, \text{cm} \) from the mirror. What is the

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. Focal length: f = -10 cm (concave mirror). Image distance: v = -20 cm (real image, same side as object). Mirror equation: (1/v) + (1/u) = (1/f) . (1/-20) + (1/u) = (1/-10) ⇒ (1/u) = (1/-10) + (1/20) = (-2 + 1/20) = (-1/20) . u =

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Reflection by Spherical Mirrors and Mirror Formula

A convex mirror of focal length \( 10 \, \text{cm} \) forms an image \( 5 \, \text{cm} \) behind the mirror. What is the

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Focal length: f = 10 cm (convex mirror). Image distance: v = 5 cm (virtual image). Mirror equation: (1/v) + (1/u) = (1/f) . (1/5) + (1/u) = (1/10) ⇒ (1/u) = (1/10) - (1/5) = (1 - 2/10) = (-1/10) . u = -10 cm . Substituting values gives 5 cm, which matches expected image

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Reflection by Spherical Mirrors and Mirror Formula

A glass slab (\( n = 1.5 \)) of thickness \( 9 \, \text{cm} \) is placed over a mark. What is the apparent shift?

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. Shift = t ( 1 - (1/n) ) . t = 9 cm , n = 1.5 . Shift = 9 ( 1 - (1/1.5) ) = 9 ( 1 - (2/3) ) = 9 × (1/3) = 3 cm . Substituting values gives 3 cm, which matches

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Reflection by Spherical Mirrors and Mirror Formula

What happens to light rays when they strike a convex mirror at an angle parallel to its principal axis?

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. In a convex mirror, rays parallel to the principal axis diverge after reflection. When traced backward, these diverging rays appear to originate from the focal point behind the mirror, which is why the focal point is virtual and located on the opposite side of the incident light. Substituting values gives They appear to diverge from the

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Reflection by Spherical Mirrors and Mirror Formula

An object is placed \( 15 \, \text{cm} \) in front of a concave mirror of focal length \( 10 \, \text{cm} \). Where is t

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. f = -10 cm , u = -15 cm . (1/v) + (1/-15) = (1/-10) ⇒ (1/v) = (1/-10) + (1/15) = (-3 + 2/30) = (-1/30) . v = -30 cm (real image). Substituting values gives 30 cm, which matches expected image position and magnification from mirror/lens

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Reflection by Spherical Mirrors and Mirror Formula

An object of height \( 2 \, \text{cm} \) is placed \( 10 \, \text{cm} \) from a concave mirror of focal length \( 5 \, \

**Concave mirror image formation** depends on object position: beyond C real inverted diminished between F and C, at C real inverted same size at C, between C and F real inverted magnified beyond C, at F image at infinity, within F virtual erect magnified behind mirror. Focal length: f = -5 cm , u = -10 cm . Mirror equation: (1/v) + (1/-10) = (1/-5) ⇒ (1/v) = (1/-5) + (1/10) = (-2 + 1/10) = (-1/10) . v = -10 cm . Magnification: m = -(v/u) = -(-10/-10) = -1 . Image height: h' = m × h = -1 × 2 = -2

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Reflection by Spherical Mirrors and Mirror Formula

An object is placed \( 12 \, \text{cm} \) from a concave mirror of focal length \( 6 \, \text{cm} \). What is the image

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Focal length: f = -6 cm , u = -12 cm . Mirror equation: (1/v) + (1/-12) = (1/-6) ⇒ (1/v) = (1/-6) + (1/12) = (-2 + 1/12) = (-1/12) . v = -12 cm (real image). Substituting values gives 12 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v

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